Calculating the percentages can be tedious, but when the success or failure of a vulnerable slam is at stake, it should be worth the effort to calculate the relative chances of success of the lines under consideration.

At the table West led the heart 10 against six no-trump, and declarer felt a rush of euphoria for having been spared a diamond lead. He won in hand, led a club to the king, cashed the club queen, then set about spades. He would be home against any normal break, since only four spade tricks were needed. Accordingly he led a spade to the queen, and a spade towards dummy and his hopes were dashed when West showed out.

Of course a 4-2 or better spade break will occur five times in six, and additionally if the spade jack or 10 fall under the queen, the combined holding of the spade eight and nine will be good enough to establish an extra trick. But declarer should also consider how to protect against one opponent or other having five chunky spades. In fact you can almost always succeed if it is East with the length. Cash one top club only, then lead a spade towards hand, inserting the eight if East plays low.

This copes with East having five spades and West holding a low singleton, or with West having five spades and East holding the singleton jack or 10. Admittedly it loses out when West has the bare spade jack or 10, but it is far the best approach over all.

Scotland won their first ever Gold Medal at bridge, at the 3rd Commonwealth Nations Bridge Championship. Today’s hand from that event sees Tony Nunn of Australia drawing inferences from the bidding and play to land his contract.

After West dealt and passed, North-South bid unopposed to four hearts, against which West led the spade queen. Nunn rose with dummy’s ace, under which East played the king, a revealing card. Declarer called for the heart five from dummy. East followed with the four and Nunn rose with the king, collecting West’s queen.

After that, the rest was relatively plain sailing. Nunn led a club to the ace, the club king, then ruffed a low club – collecting East’s queen in the process. Next came three rounds of diamonds ending in dummy, and the club jack. East did the best he could when he ruffed with the seven, and South overruffed with the jack. That was nine tricks in the bag and with three trumps left in dummy to East’s two, the game was now assured.

You might ask yourself why Nunn led to the heart king at trick two. At trick one, East had unblocked the spade king under the ace. He surely wouldn’t have done so from a three-card suit, so he had either a singleton or doubleton king, which in turn meant that West had started with at least five decent spades. If West had also held the heart ace, Nunn reckoned he might well have overcalled at his second turn, hence East had that card.

Today’s deal came up in a high standard Swiss teams event. At one table North and South settled for a contract of five clubs. The defenders led a top heart, and West shifted to a spade at trick two into the ace-queen. Declarer disconsolately claimed his 12 tricks and tried to persuade his partner that slam was against the odds, since West had been favorite to hold the spade king.

However when it came to scoring up the deal, South discovered that his side had actually gained a big swing on the deal. The auction went as shown in the diagram. West led the heart king against six clubs; what do you think happened next?

If East had left his partner on play, then even if West had not exited with a spade, declarer would surely have come home with his slam. But our East was made of sterner stuff. He overtook the heart king with his ace and played a spade. Had declarer known that diamonds were not breaking, he would have had no option but to take the spade finesse. But it was hardly unreasonable for South to play for the diamonds to break 4-2. He went up with the spade ace, and down went the slam. Declarer could draw trumps and try to ruff out the diamonds, but the bad break prevented him from establishing any pressure in the endgame, and he was left with a spade loser at trick 13.

When North raised diamonds at his first turn instead of bidding two no-trump, it made reaching the no-trump game much harder. Probing for no-trump, but worried about the hearts, South tried three clubs, but North was reluctant to bite the bullet, and South settled for the minor-suit game. Against this contract West led the heart two.

Dummy’s jack lost to the ace and a spade came back, giving nothing away. South did the best he could when he won in hand and led a trump to dummy. Then he led the club 10 from dummy at once, hoping East would forget to cover. Alas for declarer, East was on the ball, and when he covered the club 10 with the queen, South ended up losing two club tricks, to go one off.

Note that had East returned a heart at trick two, declarer simply discards a club and can set up a heart winner in dummy for his remaining club loser. But can you see a neat way for South to have improved his chances at trick one? Try playing the heart six from dummy at trick one, instead of the jack. This puts East under a lot of pressure – it could so easily be wrong for him to insert the heart eight, and so he would almost certainly have gone up with his ace. Now whatever the defenders do, declarer can establish a home for his club losers on the hearts, or the defense must play clubs themselves and achieve the same result.

At the 1996 trials the encounter between the teams captained by Edgar Kaplan and Howard Weinstein went down to the wire. With 32 boards to go Kaplan led by 19, but they lost the last two sets, and with them the match.

This board featured an unlikely game coming home with nine tricks. Weinstein doubled a weak two spade opening, and heard his partner bid two notrump — which the partnership played conventionally as a negative. This is an extension of the Lebensohl convention. Weinstein now guessed to raise to three notrump, giving his partner Ralph Katz the delight of playing the contract.

Katz won the opening spade lead in dummy, and immediately led a low heart to his hand, as East (Bart Bramley) ducked, to pass the diamond nine. Bramley won the diamond queen, and returned the club nine; Katz took his club queen, and played a heart to the ace and another heart.

Bramley took his king and got out with a low club, but Katz could win in dummy and throw Bramley in with his club winners. Bramley had two clubs to cash, but at trick 11 he was obliged to lead a diamond into dummy’s tenace for the contract, and a 10 IMP pick-up to Weinstein.

The trials were eventually won by the Robbins team, who defeated my squad in the semi-finals. They say you only remember your losses, not your victories. In this case, that is certainly true!

After the Nickell team lost the finals of the 1997 trials they had a second chance to qualify for the world championships in Tunisia. This board comes from their victory in that match over the Jacobs team, but it features a nice defense by the losers.

Brian Glubok and Sam Lev defended four spades by South after a multi two diamond opening bid. This opening bid shows a weak hand with either hearts or spades, and South arranged to be declarer by getting his partner to transfer into his major. (Warning: don’t try this at home!)

With a blind lead, Lev got the defense off on the wrong foot by leading the heart jack rather than a diamond, and now declarer was in with a chance. He rose with the king, unblocked the spade king, and played the club king, then ace, discarding a diamond. Lev followed with two middle clubs, neutral suit preference to imply no real interest in either red suit. When Glubok ruffed the second club, he carefully returned the heart queen!

This entry-destroying play (sometimes referred to as a Merrimac Coup) left declarer in hand for the last time. It allowed him to throw one more diamond loser from dummy on the third top club, but Glubok could ruff again. He could then play a third heart, to take a third ruff for the defenders, with the diamond ace to come as the fourth winner.

In this deal from the finals of the US trials the Deutsch team took the lead over the Nickell team in the middle of the match and pulled away thereafter, winning comfortably in the end. But this coup went to the Nickell team.

Both tables had an unopposed auction to four spades on the lead of the heart 10. For Deutsch, Michael Rosenberg took his king and played a club back, won in dummy for a trump finesse. Now although the defense could get a club ruff, it was with a trump winner, and declarer could discard his diamonds on dummy’s clubs.

By contrast, where Nickell was defending, Dick Freeman led the heart 10, won by Nick Nickell with the ace. Nick returned the diamond six to his partner’s king. His logic was that if his partner had the diamond king it might go away unless a diamond was played immediately, and that by his shifting to a high diamond, West should work out there was no future in the suit.

This was exactly what transpired. Freeman found the third defensive switch in three tricks, to the club four, which was won by the ace in dummy. Chip Martel played a spade to the queen, and now king and a club ruff beat the contract. It was irritating for Freeman to discover that his partner’s ruff was with a natural trump trick, but the 12 IMPS his side picked up was doubtless quite satisfying enough.

You can follow the trials this week at usbf.org.

Today’s deal from a bygone US trials saw Seymon Deutsch take on Jeff Wolfson in the semi-final stage. Both tables reached three no-trump, and Wolfson went one down on a spade lead after an unopposed auction, when he tested hearts then led the diamond queen from dummy. After the diamond queen was covered by the king, declarer tested diamonds but had only eight tricks – three tricks in each red suit and one spade on top. He could establish a second spade but had no valid route to a ninth trick.

By contrast, Chip Martel for Deutsch had the benefit of an informative auction. He won the spade 10 at trick one, and tested hearts, pitching a club from hand, then reassessed the position. He needed the diamond king onside, but since neither opponent had introduced spades, a 4-4-4-1 shape on his right was quite plausible. Playing the diamond queen would lose out to a singleton king, but if he were to play a low diamond from dummy and the king was in a three-card or longer holding, he would have had to lose an unnecessary diamond trick.

Martel correctly led a small diamond from dummy, and the appearance of the king brought him up to nine tricks; four diamonds, two spades, and three hearts.

The mathematics of the position are quite complex. But Martel believed that East had four cards in each major, and from his opening bid had at least three clubs. Therefore if he had the diamond king it had to be singleton or doubleton.

So he ran three rounds of diamonds, ending in hand, East keeping all four clubs and one spade. Now Martel played the spade king, ducked, then led a diamond to dummy, and a club toward his hand for his ninth trick. Had East kept two spades and three clubs, Martel would have built himself a club trick first before tackling spades.

On this deal from the US trials from a few years ago, Gary Cohler’s jump to three no-trump seems a reasonable if slightly premature action, since he was expecting to find his partner a doubleton spade. However a slower route of doubling and then bidding three no-trump might have led to reaching four hearts. A spade was led against three notrump, and declarer was in deep trouble. He led a diamond toward his hand but East, Jim Krekorian took the diamond ace to continue spades, and Cohler took the third round. Now if Cohler could have divined the heart position, he would have made the hand (which would certainly not have been impossible, given East’s decision to take the diamond ace with non-solid spades. Surely he figured to have the heart card). However Cohler played for the heart king to be onside, leading the heart queen from hand hoping that he could duck the trick to the West hand. That led to two down.

In the closed room, Neil Chambers as North played four hearts on the spade lead, which established a home for his club loser. Since declarer could see that he had to lose two diamond tricks, his target became to hold the heart losers to one. Chambers made no mistake, playing off the heart ace to drop the singleton king, the only relevant 4-1 split, and made his game.

You can follow a summary of the trials on usbf.org, and watch live at online.bridgebase.com